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If there are two interacting subsystems A and B, how to define the information flow from A to B in quantum regime and classical regime?

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  • $\begingroup$ In the classical regime information flow is most commonly defined via the transfer entropy. For a nice physical perspective see Horowitz and Esposito, 2014. For the quantum case I have no idea. $\endgroup$ – Nathaniel Mar 20 '17 at 3:12
  • $\begingroup$ In general classical probability, I am not aware of a good definition of a causal-type information flow. Transfer entropy is problematic because it does not capture causality correctly (see e.g. Ay & Polani 2008). The problem is now increasingly addressed under the framework of Partial Information Decomposition, following a seminal paper by Beer & Williams. See for instance the series of papers by Bertschinger, Rauh, Olbrich et al. However, it might be that for a physical system with phase space volume conservation and microreversibility, stronger statements are possible. $\endgroup$ – Captain Emacs Nov 25 at 0:11
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One way to quantify the flow of quantum information under evolution by a unitary operator is the so-called flow or index of the unitary, as in

Kitaev, Anyons in an exactly solved model and beyond (2006), https://arxiv.org/pdf/cond-mat/0506438.pdf

Gross, Nesme, Vogts, Werner, Index theory of one dimensional quantum walks and cellular automata (2012), https://arxiv.org/pdf/0910.3675.pdf

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In classical physics information flows between systems when the measurable quantities of one system depend on those of another, e.g. the frequency at which a weight bobs on the end of a spring will depend on the Young's modulus of the spring.

In quantum physics, information flow can be characterized by dependence of the observables of one system on those of another. The observables of one system can depend on those of another although it is impossible to tell by measuring either system alone: this is called locally inaccessible information.

See Information Flow in Entangled Quantum Systems.

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  • $\begingroup$ But what if we want to characterise the flow between a quantum system and a thermal bath(eg. environment) which cannot be measured? $\endgroup$ – yangcs11 Mar 23 '17 at 2:47
  • $\begingroup$ In that case, you do the same kind of calculation as explained in the linked paper and then disregard the qubits representing the bath. $\endgroup$ – alanf Mar 23 '17 at 8:24

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